Problem: Solve for $x$ : $7\sqrt{x} + 9 = 4\sqrt{x} + 5$
Answer: Subtract $4\sqrt{x}$ from both sides: $(7\sqrt{x} + 9) - 4\sqrt{x} = (4\sqrt{x} + 5) - 4\sqrt{x}$ $3\sqrt{x} + 9 = 5$ Subtract $9$ from both sides: $(3\sqrt{x} + 9) - 9 = 5 - 9$ $3\sqrt{x} = -4$ Divide both sides by $3$ $\frac{3\sqrt{x}}{3} = \frac{-4}{3}$ Simplify. $\sqrt{x} = -\dfrac{4}{3}$ The principal root of a number cannot be negative. So, there is no solution.